In SIDH and SIKE protocols, public keys are defined over quadratic extensions
of prime fields. We present in this work a projective invariant property
characterizing affine Montgomery curves defined over prime fields. We then
force a secret 3-isogeny chain to repeatedly pass through a curve defined over
a prime field in order to exploit the new property and inject zeros in the
A-coefficient of an intermediate curve to successfully recover the isogeny
chain one step at a time. Our results introduce a new kind of fault attacks
applicable to SIDH and SIKE.